1. Field of the Invention
The present invention relates to a data processing apparatus and a data processing method for a series of numerical data in a system to be an object (for example, apparatus and analytical data).
2. Description of the Related Art
Various models have been proposed as techniques for performing data smoothing and data prediction to a series of numerical data in a system to be an object. For understanding a state of a system to be an object, differential processing, such as a first order differential or a second order differential, is sometimes used in order to detect the extreme values (maximum value and minimum value) that are change points of data, or an inflection point. In particular, in a case of time series data, such as measurement data including for example noise, performing high-precision data smoothing processing and differential processing so as to detect a change point in a system to be an object and to control the system to be an object, has been an important technical problem.
Techniques for performing data smoothing and data prediction in the related art include, for example, a curve fitting method and a moving average method as described in K. Takahashi, “Inside Data Processing”, Journal of Surface Analysis, Vol. 7, No. 1, 2000, pp 68-77. Examples of a curve fitting method include a polynomial fitting method (Savitzky-Golay method) as described in JP 2000-228397 A. Examples of a digital filter include Butterworth low pass filter. Examples of a moving average method include an exponential smoothing method as described in A. C. Harvey, “TIME SERIES MODELS”, translated by N. Kunitomo and T. Yamamoto, The University of Tokyo Press, 1985, p. 173.
A. C. Harvey, “TIME SERIES MODELS”, translated by N. Kunitomo and T. Yamamoto, The University of Tokyo Press, 1985, p. 173 discloses a simple exponential smoothing method (one smoothing parameter) and a double exponential smoothing method (two smoothing parameters). These methods are used in the field of economic relationship, such as supply and demand forecasting. James W Taylor, Journal of Forecasting, 2004, (23), pp 385-394 discloses an adaptive simple exponential smoothing method in which a smoothing coefficient varies in accordance with input data (in particular, sequential input data). A case where the smoothing coefficient varies in accordance with |a relative error/an absolute error| and a case where the smoothing coefficient varies in accordance with a logistic function, have been described. Typically, as expressed by Expressions (1) to (4), a case where a smoothing coefficient varies in accordance with |a relative error/an absolute error|, is sometimes used.Smoothing of data: S1t+1=α1tY1t+(1−α1t)S1t   Expression (1)Smoothing coefficient: α1t=|δαt/Δαt|  Expression (2)Relative error: δαt=A1|(Y1t−S1t)+(1−A1)Δαt−1   Expression (3)Absolute error: Δαt=A1|Y1t−S1t|+(1−A1)Δαt−1   Expression (4)
Here, input data is defined, for example, as time series data Y1t: t=1, 2, . . . , and a predicted value of smoothing of data of one-period prediction output is defined as St+1. Symbol A1 denotes an arbitrary constant. Note, each of the symbols is different from each of those in James W Taylor, Journal of Forecasting, 2004, (23), pp 385-394. However, the symbols are described so as to be similar to those in the following embodiments as much as possible.
Techniques for performing data differential processing in the related art, sometimes use a difference method. The polynomial fitting method (Savitzky-Golay method) may be used as described in JP 2000-228397 A and Peter A. Gorry, Anal. Chem. 1990, (62), pp 570-573. Typically, a polynomial fitting method (Savitzky-Golay method) sometimes uses a series of a plurality of pieces of data so as to derive a differential processing result at the center point of a period of the series of a plurality of pieces of data. However, Peter A. Gorry, Anal. Chem. 1990, (62), pp 570-573 discloses a method in which the polynomial fitting method (Savitzky-Golay method) performs data smoothing processing and a first order differential processing at an arbitrary point of data to be used.
As an example of performing data smoothing processing to time series data, such as measurement data including, for example, noise, performing a first order differential processing and a second order differential processing so as to detect a change point of the data, and controlling a system to be an object, JP 1986-53728 A discloses a method for performing data smoothing processing to spectral intensity signal data from plasma emission by moving average processing, and determining an etching end point with a first order differential value and a second order differential value. James W Taylor, Journal of Forecasting, 2004, (23), pp 385-394 discloses a method for estimating an optimum smoothing parameter by minimizing a total sum of errors of a one-period predicted value by the simple exponential smoothing method.